AC motor control system

ABSTRACT

A method of controlling an AC motor which exhibits a constant torque characteristic at a rotational speed N below a base speed Nb and a constant output characteristic at a rotational speed N above the base speed Nb, comprising the steps of finding a base speed N L  after limiting the output power of the AC motor, N L  being derived from the base speed Nb and the ratio η between maximum output power Pmax 1  and maximum output power Pmax 2  before and after the output power of the AC is limited, respectively, rendering the slip frequency of the AC motor constant until the rotational speed N of the AC motor reaches the base speed N L , varying the slip frequency in inverse proportion to the rotational speed N for N between N L  and Nb (N L  &lt;N≦Nb), and varying the slip frequency in proportion to the rotational speed N for N above Nb (Nb&lt;N), whereby the output power of the AC motor is rendered constant at a rotational speed N above N L .

This is a divisional of co-pending application Ser. No. 438,692 filed onNov. 2, 1982, now U.S. Pat. No. 4,499,414.

BACKGROUND OF THE INVENTION

This invention relates to an AC motor control system and, moreparticularly, to an AC motor control system in which a region ofconstant output power can be enlarged in cases where the AC motor outputpower is limited in magnitude.

AC motors (induction motors) develop a constant output (constant outputcharacteristic) at speeds above a certain constant speed (base speed),and develop a constant torque (constant torque characteristic) at speedsbelow the base speed. This may be understood from FIG. 1, which showsthe characteristics of an AC motor. The solid line indicates the outputpower (KVA)-speed characteristic, and the broken line the torque-speedcharacteristic. Nb indicates the base speed. In AC motors of this kind,the following three advantages would manifest themselves if it werepossible to decrease the AC motor output power with a decrease in loadand widen the region of the constant output characteristic:

(1) the power supply output (KVA) can be reduced in proportion to theoutput power of the AC motor, making it possible to reduce the powersupply capacity for small loads even if the capacity of the AC motor islarge;

(2) the number of gear stages can be reduced in cases where the AC motoris employed as a spindle motor in a small-size machining center; and

(3) in the constant peripheral speed control of a lathe or the like,cutting can be performed while exploiting the output power of the motorto the maximum extent by widening the region of the constant outputcharacteristic.

Hereinafter, control executed for the purpose of reducing AC motoroutput power in accordance with the size of a load and widening theconstant output characteristic region shall be referred to as outputlimitation control.

If we assume that a voltage-speed characteristic is as represented bythe solid line in FIG. 2 without application of output limitationcontrol, then the desired characteristic would be as shown by thedot-and-dash line if output limitation control were applied. Withmethods according to the prior art, however, the output-speedcharacteristic actually obtained is as depicted by the dashed line, evenwith output limitation control. It will be appreciated that the regionof constant output power cannot be widened significantly according tothe prior art, making it impossible to realize the three advantages setforth above.

SUMMARY OF THE INVENTION

Accordingly, an object of the present invention is to provide a novel ACmotor control system which enables a region of constant output power tobe enlarged when limiting the output of an AC induction motor.

Another object of the present invention is to provide an AC motorcontrol system which enables the magnitude of AC motor output power tobe changed in accordance with the motor load, and which also makes itpossible to broaden the range of speeds over which the magnitude of theAC motor output power is constant.

A further object of the present invention is to provide an AC motorcontrol system with which the capacity of a power supply can be reducedin accordance with the size of the AC motor load even if the AC motoritself is large in capacity, and with which a very efficient cuttingoperation can be performed wherein the AC motor power is utilized to thefullest extent.

Other features and advantages of the invention will be apparent from thefollowing description in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph of the characteristics of an AC motor;

FIG. 2 is a graph of the characteristics of an AC motor in accordancewith a conventional control method;

FIGS. 3A and 3B are graphs of an AC motor output-speed characteristicand slip frequency-speed characteristic, respectively, for describingthe method used by the present invention;

FIG. 4 is a circuit diagram of an AC motor equivalent circuit;

FIG. 5 is a graph of a characteristic curve for a case where the valueset in a slip counter is plotted against the speed of an AC motor; and

FIG. 6 is a block diagram of an embodiment for practicing the method ofthe present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

A region of a constant torque characteristic, where motor speed is lessthan the natural base speed Nb (about 1500 rpm), exhibits a constantslip frequency. In other words, this is a region wherein an AC motor issubjected to so-called vector control, in accordance with which bothfrequency and effective value of the motor primary voltage arecontrolled. On the other hand, a region of constant outputcharacteristic, where motor speed is greater than the base speed Nb, isone where slip control is applied so that slip may take on a constantvalue. FIG. 3A shows the output-speed characteristic of an AC motor andFIG. 3B the slip frequency-speed characteristic thereof, wherein thesolid lines in both diagrams indicate the prevailing conditions in theabsence of output limitation control, while the dot-and-dash linesrepresent application of output limitation control.

Reference will be made to FIGS. 3A and 3B to describe a control methodin accordance with the present invention through which the outputcharacteristic of an AC motor will follow the curve indicated by thedot-and-dash line (FIG. 3A) when the maximum power of the motor ischanged from Pmax₁ to Pmax₂ by applying output limitation control.

Pmax₁ is the maximum output power obtainable at a base speed, e.g., 1500rpm, which is a rotational speed on the order of one-third the maximummotor speed. Pmax₂ is motor + amplifier maximum output power in a casewhere the motor is used after lowering the base speed by reducingmaximum motor output power by a servo unit (servoamplifier). In otherwords, Pmax₂ is the maximum output power which, by lowering the basespeed through an intentional reduction in the obtainable motor output,makes it unnecessary to effect a changeover of gears or the like.

First, the ratio η of Pmax₂ to Pmax₁ (referred to as the limiting ratio)and a new base speed N_(L) following output limitation control are foundfrom the following equations:

    η=Pmax.sub.2 /Pmax.sub.1                               (1)

    N.sub.L =η·Nb                                 (2)

The next step is to exercise control in such fashion that the slipfreqency will remain constant up to new base speed N_(L) following thisoutput limitation control (see region AR in FIG. 3B). This will causethe AC motor output power P to rise linearly as shown by thedot-and-dash line in region AR1 of FIG. 3A. The reason is that theoutput power P and torque T are related as follows:

    P=wT                                                       (3)

with the torque T being constant for rotational speeds between 0 andN_(L). It should be noted that w is the angular frequency (correspondingto rotational speed) of the AC motor, wherein w=2πN (N standing for therotational speed of the motor). Stated another way, in a region ofvector control where the torque is constant, the torque can be expressedas follows:

    T=k(r.sub.2 I.sub.2 /sw)I.sub.2 =a constant                (4)

in which r₂ I₂ /sw is the factor rendered constant by the controloperation. Thus, in a region where vector control is applied, the torqueT is so controlled as to be proportional to the secondary current I₂. InEq. (4), k indicates a constant, r₂ the secondary resistance, s theslip, s·w the slip frequency, and I₂ the secondary current. Accordingly,for a rotational speed N ranging from 0 to N_(L), the following relationholds:

    T∝I.sub.2 ∝s·w=f.sub.1s =a constant (5)

so that the slip frequency f_(1s) (=s·w) is constant within said rangeof speeds from 0 to N_(L). The symbol ∝ in the above equation indicatesa proportional relation. In other words, if the slip frequency f_(1s)(=s·w) is rendered contant in a region of vector control, then thetorque will be rendered constant and the output power P will beproportional to the motor speed, the latter following from Eq. (3).

The next step is to find the slip frequency f_(1s), at the base speed Nband then vary the slip frequency from f_(1s) to f_(1s), within the rangegiven by N_(L) ≦N≦N_(b), which change in slip frequency will beinversely proportional to the change in rotational speed N. By doing so,the output power will be held constant within said range N_(L) ≦N≦N_(b).More specifically, since the output power P must be so controlled as tobe constant within the range N_(L) ≦N≦N_(b), the required condition isthat the following hold, from Eq. (3):

    T∝1/w                                               (6)

Since vector control is in effect within the range 0≦N≦N_(b), the torqueis expressed by Eq. (4) so that the following holds:

    r.sub.2 I.sub.2 /s·w=a constant                   (7)

Therefore, from Eqs. (4), (6) and (7), we have:

    T=k(r.sub.2 I.sub.2 /s·w)I.sub.2 ∝I.sub.2 ∝1/w (8)

Furthermore, the following will hold from Eq. (7):

    I.sub.2 ∝s·w (=f.sub.s)                    (8')

giving the following from Eqs. (8) and (8'):

    f.sub.s ∝1/w                                        (9)

where f_(s) stands for the slip frequency and f_(s) =s·w. Thus thesecondary current I₂ and slip frequency f_(s) are both inverselyproportional to the motor speed N (=2πw), and the slip frequency f_(1s')at the base speed Nb is given by:

    f.sub.1s' =η·f.sub.1s                         (10)

To render the output power P constant at Pmax₂ within the range N_(L)≦N≦N_(b) in the foregoing, the slip frequency should be controlled ininverse proportion to the rotational speed N from f_(1s) t f_(1s'), asshown in region AR2 of FIG. 3(B).

Finally, in the slip region where Nb N holds, the slip s' followingoutput limitation control is found from the following equation, usingthe slip s that prevails prior to output limitation control as well asthe limitation ratio η:

    s'=η·s                                        (11)

If control is so exercised as to render the slip s' constant, then themaximum output power can be held constant at Pmax₂. More specifically,referring to the equivalent circuit of an induction motor as shown inFIG. 4, voltage E_(m) is constant in the slip region and is given by:

    E.sub.m =w·l.sub.m ·I.sub.o =r.sub.2 I.sub.2 /s=a constant                                                  (12)

where I_(o) represents the excitation current. The torque T, meanwhile,can be expressed as follows:

    T=3P.sub.n ·l.sub.m ·I.sub.o ·I.sub.2 (13)

where P_(n) represents the number of poles. From Eqs. (12) and (13) wecan write:

    T∝3P.sub.n l.sub.m (1/w)·I.sub.2           (14)

since I₂ ∝s from Eq. (12), we have:

    T∝s/w                                               (15)

Thus, in the slip region, the torque T decreases in inverse proportionto the motor speed but in proportion to the slip s. Furthermore, sinceP=wT, from Eq. (15) we have:

    P∝s=a constant                                      (16)

indicating that the magnitude of the power P is dependent upon themagnitude of the slip s. Accordingly, if the slip s' in a case where theoutput power is limited is made a multiple η of the slips when outputlimitation control is not applied (where η<1), then the output power inthe slip region can be maintained as the desired value of Pmax₂, asshown in region AR3 of FIG. 3A.

In summary, the method of the present invention includes steps offinding the new base speed N_(L) after the application of outputlimitation control, N_(L) being derived from the base speed Nb and theratio (limitation ratio) η between the maximum output power Pmax₁ andthe maximum output power Pmax₂ before and after output limitationcontrol is applied, respectively, controlling the rotational speed N ofthe AC motor in such a manner that the slip frequency is renderedconstant within the range 0≦N≦N_(L), varying the slip frequency ininverse proportion to the rotational speed N within the region N_(L)≦N≦N_(b), and varying the slip frequency in proporton to the rotationalspeed N in the region Nb<N, that is, holding the slip constant in saidregion. Following these steps will result in an output-speedcharacteristic as shown by the dot-and-dash line of FIG. 3A, wherein itwill be seen that the region of constant output power is broadened up toN_(L).

The following steps (a) through (g) explain the processing that isexecuted for obtaining the characteristic given by the dot-and-dash lineof FIG. 3A upon limiting the output power from Pmax₁ to Pmax₂.

(a) The limitation ratio η is found from Eq. (1).

(b) The new base speed N_(L) following the application of outputlimitation control is found from Eq. (2). It should be noted that thebase speed NB before output limitation is a known quantity, such as 1500rpm.

(c) The slip frequency f_(1s') at the base speed Nb and the slip s' inthe slip region are found from Eqs. (10) and (11), respectively.

(d) A relation involving the slip frequency f_(s) in the base speedrange from N_(L) to Nb is determined. Specifically, f_(s) can beexpressed by the following:

    f.sub.s =a/N+b                                             (17a)

Since f_(s) =f_(1s) when N=N_(L), and since f_(s) =f_(1s') =η·f_(1s), arelation involving the slip frequency f_(s) in the region N_(L) ≦N<N_(b)is determined when the above values for f_(s) are substituted in Eq.(17a) to find a and b. Here a and b are given by the following:

    a=f.sub.1s (1-η)N.sub.L ·Nb/(Nb-N.sub.L)      (17b)

    b=f.sub.1s (η·Nb-N.sub.L)                     (17c)

(e) A correspondence table between the slip frequency f_(s) and therotational speed N is created using Eqs. (17a) through (17c), and thetable is stored in memory.

(f) The rotational speed N is sensed and the slip frequency f_(s) isfound from the correspondence table.

(g) Thenceforth a three-phase primary voltage is generated through knownmeans.

Note that an arrangement is possible wherein, in place of steps (e) and(f), the slip frequency is computed on each occasion by using Eq. (17a)and a, b obtained from step d. An alternative arrangement, which will bedescribed in greater detail below, is to obtain and store beforehand acorrespondence table between the rotational speed N and a value S_(v) tobe set in a slip counter, read a prescribed set value S_(v) conformingto the rotational speed out of the correspondence table and set saidvalue in the slip counter, and frequency-divide clock pulses of apredetermined frequency F by this set value S_(v) to obtain the slipfrequency.

FIG. 5 shows the correspondence between the rotational speed N and thevalue S_(v) set in the slip counter. It will be seen that: S_(v) =A inthe range of speeds 0≦N≦N_(L) ; S_(v) =B·N in the range of speeds N_(L)<N≦Nb; and S_(v) =C/N in the range of speeds N_(b) <N, where A, B and Care constants. As a result, a slip frequency f_(s) obtained byfrequency-dividing clock pulses of a fixed frequency F by the set valueS_(v) will be given by: f_(s) =F/A (a constant) for 0<N<N_(L) ; f_(s)=F/B·N, which is inversely proportional to the rotational speed N, forN_(L) <N<Nb; and f_(s) =FN/C, which is proportional to the rotationalspeed N, for Nb<N. By suitably deciding the constants A, B and C,therefore, the slip frequency f_(s) can be made to vary as indicated bythe dot-and-dash line of FIG. 3B.

Reference will now be had to the block diagram of FIG. 6 to describe anarrangement for practicing an AC motor control method in accordance withthe present invention.

Numeral 11 denotes the AC motor, e.g., induction motor. The arrangementfor controlling the motor includes a pulse generator 12 for generatingfirst and second pulse trains P1, P1 displaced in phase from each otherby π/2 and having a frequency f_(v) proportional to the speed of the ACmotor, and a quadrupling circuit 13 which differentiates the first andsecond pulse trains P1, P2 from the pulse generator 12 for producing apulse train P_(v) where the frequency F_(v) thereof is four times thefrequency f_(v) (i.e., F_(v) =4·f_(v)). The quadrupling circuit 13 alsoproduces a rotational direction signal RDS upon discriminating the phasedifference between the first and second pulses trains P1, P2. A countercircuit 14 counts the pulses in the pulse train P_(v) and is reset eachtime its content is read at predetermined time intervals by a processor,described later, whereupon the counter circuit counts the pulses Pvagain starting from zero. More specifically, the value of the countwithin the counter circuit 14 represents the actual rotational speed nof the AC motor 11, namely the angular frequency w_(n). The arrangementalso includes a microcomputer 15 having a processor 15a, a controlprogram memory 15b, a RAM serving as a data memory 15c, and a ROMserving as a correspondence table memory 15d. The correspondence tablememory 15d has a first storage area 15d-1 for storing the correspondingrelationship between n_(s), namely the difference between a commandedspeed n_(c) and the actual motor speed n, and amplitude I₁, a secondstorage area 15d-2 for storing the corresponding relationship betweenn_(s) and a phase difference φ, and a third storage area 15d-3 forstoring the corresponding relationship between the actual speed n andvalue S_(v) to be set in a slip counter 16. The control program memory15b stores a control program for administering a variety of computationsand control operations. Under the control of the control program, themicrocomputer 15 computes the difference n_(s) between the commandedspeed n_(c), which enters from a commanded speed generating circuit (notshown), and the actual speed n, and reads, from the first, second andthird storage areas, the amplitude I₁ and phase difference φcorresponding to the difference n_(s), as well as the set value S_(v)corresponding to the actual speed n. The microcomputer 15 delivers thesevalues as output signals. The above-mentioned slip counter 16 is apresettable counter in which the value S_(v) is loaded00, the counterbeing adapted to generate pulses P_(s) indicative of the slip angularfrequency w_(s) (=2πf_(s)) by frequency-dividing a clock pulse train CLPby the set value S_(v). By way of example, letting the set value S_(v)be m, a single slip pulse P_(s) will be produced upon the generation ofm-number of clock pulses CLP. In other words, the slip counter 16divides the frequency F of the clock pulses CLP by m to produce a pulsetrain P_(s) having the slip frequency f_(s), namely F/m. It should benoted that this frequency division operation brings the slip angularfrequency w_(s) into conformance with the angular frequency w_(n) of themotor speed. A presettable counter circuit 17 is set to the phasedifference φ and is adapted to produce a pulse train Pφ of a frequencycommensurate with the phase difference. A mixing circuit 18 combines (a)the pulse train P_(v) from the quadrupling circuit 13, the pulse trainindicating an angular frequency w_(n) conforming to the actual speed ofthe motor 11, (b) the pulse train P_(s) from the slip counter 16,indicative of the slip angular frequency w_(s), and (c) the pulse trainPφ from the counter circuit 17, having a frequency commensurate with thephase difference φ.

The arrangement is also provided with an up/down counter 19 forreversibly counting the pulses from the mixing circuit 18 in accordancewith the sign of the pulses. Note that the status of the up/down counter19 at any given time will be a numerical value N corresponding townt+wst+φ. A signal from the up/down counter 19 indicative of N isapplied to three decoders 20, 21, 22. These decoders 20, 21, 22 havecorrespondence tables establishing correspondence between N and sin N,sin (N+2π/3), and sin (N+4π/3), respectively. The decoders receive thenumerical value N as a high-rate input and successively producerespective U-, V- and W-phase current commands (digital values) I_(U),I_(V), I_(W) commensurate with the numerical value N. Adigital-to-analog converter (referred to hereinafter as a DA converter)23 receives the signal indicative of the amplitude I₁ from themicrocomputer 15. Multiplying-type DA converters 24, 25, 26 receive IU,IV and IW, respectively, as well as the output of the DA converter 23.The latter is operable to convert the amplitude I₁, which is a digitalvalue, into an analog voltage proportional to I₁. The multiplying-typeDA converters 24 through 26 are adapted to multiply the three-phasecurrent command values I_(U), I_(V), I_(W) by the amplitude I₁ andconvert the results into respective analog signals to generatethree-phase analog current commands, namely:

    i.sub.u =I.sub.1 sin (w.sub.n t+w.sub.s t+φ)           (18)

    i.sub.v =I.sub.1 sin (w.sub.n t+w.sub.s t+φ+2π/3)   (19)

    i.sub.w =I.sub.1 sin (w.sub.n t+w.sub.s t+φ+4π/3)   (20)

The arrangement further includes an induction motor drive circuit 27composed of a pulse width modulator, inverter circuitry and the like,which are not shown. Power transistors constructing the invertercircuitry are switched on and off by the output of the pulse widthmodulator for supplying the induction motor 11 with three-phase current.A line L is a feedback line for a current minor loop. Designated at 28is a data input unit.

In operation, the data input unit 28 supplies the microcomputer 15 withthe maximum output power Pmax₂ after the application of outputlimitation control. It should be noted that the maximum output powerPmax₁ without the limitation on output, the base speed Nb, the slipfrequency f_(1s) in the region where the slip frequency is constant, andthe slip s in the region of where the slip is constant, have alreadybeen stored in the data memory 15c. Upon receiving the maximum outputpower Pmax₂, the microcomputer 15 executes the above-described steps (a)through (d) under the control of the control program for generating thecorrespondence table between the rotational motor speed N and the valueS_(v) set in the slip counter 16. The table is stored in thecorrespondence table memory 15d. When the speed command generating means(not shown) issues a speed command n_(c) under these conditions, thethree-phase induction motor 11 attempts to rotate at the speed n_(c).With rotation of the motor 11, the pulse generator 12 generates thefirst and second pulse trains P1, P2 displaced in phase by π/2, thefrequencies whereof are proportional to the actual rotational speed n ofthe motor 11. The quadrupling circuit 13 quadruples these pulse trainsP1, P2 to produce the pulse train P_(v) indicating the angular frequencyw_(n), and also produces the rotational direction signal RDS. The pulsetrain P_(v) is fed into the mixing circuit 18 and the counter circuit14, where the pulses are counted. The value of the count in countercircuit 14 is a numerical value corresponding to the rotational speed nof the motor, and is read out of the counter circuit at a predeterminedsampling period by the processor 15a. The processor 15a then proceeds tocompute the difference n_(s) between the commanded speed n_(c) and therotational speed n, and to fetch from the first, second and thirdstorage areas 15d-1, 15d-2, 15d-3 of the correspondence table memory 15dthe amplitude I1 and phase difference φ corresponding to the differencen_(s), as well as the set value S_(v) corresponding to the actual motorspeed n. The signals indicative of I₁, φ and S_(v) are applied to the DAconverter 23, counter circuit 17 and slip counter 16, respectively. As aresult, the slip counter 16 produces the pulse train P_(s) indicative ofthe slip angular frequency w_(s) decided by the characteristic havingthe appearance of the dot-and-dash line in FIG. 3B, and the countercircuit 17 produces the pulse train P.sub.φ corresponding to the phasedifference φ. The pulse trains P_(s), P.sub.φ are combined by the mixingcircuit 18 with the pulse train P_(v) of the angular frequency w_(n)corresponding to the actual motor speed n. The pulse train output of themixing circuit 18 enters the up/down counter 19 where the pulses arecounted up or down in accordance with their sign. The content of theup/down counter 19 is the numerical value N, which corresponds to w_(n)t+w_(s) t+φ. The decoders 20 through 23 receive the numerical value Nand, using the internal correspondence tables N-sin N, N-sin (N+2π/3)and N-sin (N+4π/3), supply the multiplying-type DA converters 24 through26 with the U-, V- and W-phase current commands I_(U), I_(V), I_(W),respectively. As a result, the DA converters 24 through 26 generate thethree-phase analog current commands i_(u), i_(v), i_(w), expressed byEqs. (18) through (20), using the amplitude signal I₁ from the DAconverter 23, as well as the current commands I_(U), I_(V), I_(W). Theanalog current commands are fed into the induction motor drive circuit27. The latter pulse-modulates the signals i_(u), i_(v), i_(w) andsupplies the induction motor 11 with three-phase current produced byswitching the power transistors of the inverter circuitry on and off inaccordance with the output of the internal pulse modulator. Thereafter,the control operation proceeds in the same manner to regulate the slipfrequency in accordance with the motor speed, as shown by thedot-and-dash line in FIG. 3B, the output power being rendered constantabove the base speed N_(L) to widen the region of constant output power,as indicated by the dot-and-dash line in FIG. 3A.

According to the present invention as described and illustratedhereinabove, the region over which the output power in constant can bewidened when limiting the output of an AC motor, enabling the capacityof the power supply to be reduced even for an AC motor of a largecapacity. Since the invention reduces the number of gear stages that arenecessary, moreover, such machine tools as a machining center can bemade smaller in size. The invention also makes it possible to carry outa cutting operation wherein the output power of the AC motor is utilizedto the fullest extent.

As many apparently widely different embodiments of the present inventionmay be made without departing from the spirit and scope thereof, it isto be understood that the invention is not limited to the specificembodiment thereof except as defined in the appended claims.

What we claim is:
 1. An induction motor control system, comprising:firstpulse means, coupled to the motor, for producing an actual speed of themotor; computing means, operatively connected to said first pulse meansand to receive a speed command, for computing a difference speed fromthe actual speed and the speed command; correspondence table means,operatively connected to said computing means, for outputting a currentamplitude and a phase difference in dependence upon the difference speedand a slip value in dependence upon the actual speed and the speedcommand said slip value is divided into first through third ranges wherethe slip value is constant in the first range, increases proportionatelywith speed in the second range and decreases inverse proportionatelywith speed in the third range; second pulse means, operatively connectedto said correspondence table means and said second pulse means, forproducing compensation pulses in dependence upon the phase differenceand the slip value output by said correspondence table means and thespeed pulses output by said first pulse means; and converting means,operatively connected to said second pulse means, said correspondencetable means and the motor, for converting the current amplitude and thecompensation pulses into motor drive currents.